Let us conclude this section by reminding the reader that the theory of Bernoulli percolation is now well developed, with a decent understanding of the properties of the scaling limit [1]}, of crossing probabilities [2]}, [3]}, universal critical exponents [4]}, scaling relations [5]}, [6]}, noise sensitivity and near-critical window [7]}, [8]}, etc. For a variant of the model (site percolation on the triangular lattice), the existence of the scaling limit and its conformal invariance was proved [9]} and critical exponents have been computed [10]}, see [11]} and references therein for an overview of two-dimensional Bernoulli percolation. Deriving all these properties for Bernoulli percolation relies on specific features, such as independence of the states of different edges and geometric interpretations of differential formulae using so-called pivotal events. These features are not satisfied for more general random-cluster models.
Another more prosaic goal of this paper is therefore to develop robust tools enabling one to bypass these special characteristics of Bernoulli percolation to extend the results mentioned in the abstract to the whole regime of critical random-cluster models undergoing a continuous phase transition. As such, these tools may have a number of implications that are not mentioned in the present paper, in particular for the study of other planar dependent percolation models.
